4 - Decentralized optimization
Published online by Cambridge University Press: 05 June 2014
Summary
A major practical and theoretical issue in the design of communication networks concerns the extent to which control can be decentralized. Over a period of time the form of the network or the demands placed on it may change, and routings may need to respond accordingly. It is rarely the case, however, that there should be a central decision-making processor, deciding upon these responses. Such a centralized processor, even if it were itself completely reliable and could cope with the complexity of the computational task involved, would have its lines of communication through the network vulnerable to delays and failures. Rather, control should be decentralized and of a simple form: the challenge is to understand how such decentralized control can be organized so that the network as a whole reacts sensibly to fluctuating demands and failures.
The behaviour of large-scale systems has been of great interest to mathematicians for over a century, with many examples coming from physics. For example, the behaviour of a gas can be described at the microscopic level in terms of the position and velocity of each molecule. At this level of detail a molecule's velocity appears as a random process, with a stationary distribution as found by Maxwell. Consistent with this detailed microscopic description of the system is macroscopic behaviour, best described by quantities such as temperature and pressure. Similarly, the behaviour of electrons in an electrical network can be described in terms of random walks, and yet this simple description at the microscopic level leads to rather sophisticated behaviour at the macroscopic level: the pattern of potentials in a network of resistors is just such that it minimizes heat dissipation for a given level of current flow.
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- Stochastic Networks , pp. 85 - 107Publisher: Cambridge University PressPrint publication year: 2014